Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 3θ

Take a quick peek at
that's how you test for the y-axis, x-axis and origin

recall your symmetry identities, cos(- θ) = cos(θ)

so, simply replace θ for those values, and if the resultant function looks exactly like the original, then it has that symmetry.